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A260711
Numbers of the form x^2 - y^2 with x >= y; x and y are odd, x + y is a power of 2.
0
0, 8, 16, 32, 48, 64, 96, 128, 160, 192, 224, 256, 320, 384, 448, 512, 576, 640, 704, 768, 832, 896, 960, 1024, 1152, 1280, 1408, 1536, 1664, 1792, 1920, 2048, 2176, 2304, 2432, 2560, 2688, 2816, 2944, 3072, 3200, 3328, 3456, 3584, 3712, 3840, 3968, 4096, 4352, 4608, 4864
OFFSET
1,2
COMMENTS
These binomials do not have primitive factors.
PROG
(Magma) lst:=[0]; r:=4864; t:=1; d:=func<t | Floor(r/(4*t))>; while d(t) gt t do s:=d(t); if s mod 2 eq 1 and t mod 2 eq 1 then s-:=1; end if; if s mod 2 eq 0 and t mod 2 eq 0 then s-:=1; end if; repeat; m:=(s+t)^2-(s-t)^2; if PrimeDivisors(s) eq [2] then Append(~lst, m); end if; s-:=2; until s-t lt 1; t+:=1; end while; Sort(lst); // Arkadiusz Wesolowski, Dec 19 2020
CROSSREFS
Subsequence of A008590.
Sequence in context: A219547 A259751 A106841 * A139598 A137243 A360124
KEYWORD
nonn
AUTHOR
STATUS
approved